What was the ratio of African Americans to Whites in the 1700s?]
Please note that the answer to this would be different for different colonies (and later states) and it would be different at different points in the 1700s. The Southern colonies, of course, would have a much higher ratio of African Americans to whites. In fact, South Carolina was majority black through much of the 18th century.
In the first census taken of the population of the United States in 1790, the slave population plus "all other free persons" who were not white was about 750,000. This was out of a total population of almost 3.9 million. This would give us a ratio of about 4.2 whites to every black person. These numbers can be found in the link below.
For another snapshot, census data tells us that it 1740, the New England colonies were 2.9% black, the Middle Colonies were 7.5%, the Upper South was 28.3% and the Lower South was 46.5%. These numbers (source: America: A Narrative History Fifth Edition p. 121) do not tell us the total populations of each region so we cannot get a ratio for the colonies as a whole. However they do give us some idea as to what the racial mixture in the colonies was at that time.